This article is a response to Dr. Serge Gracovetsky’s presentation to the Rolf Institute Annual Meeting in 2008 in Boulder, Colorado. Because it is the job of Rolfers to understand healthy function of the muscular/skeletal system, as well as to observe the impediments to it, we are interested in a comprehensive model of walking that explains what that is. We, the authors, believe that maps and models influence our perceptions and our behaviors. In the interest of finding a model of understanding the complex coordination of human ambulation that could serve our profession, we wish to raise some points in which Gracovetsky’s model and our model seem to differ. We cannot presume to assess the full breadth and depth of Gracovetsky’s knowledge on this subject, and there are many places of agreement that we will not be elucidating.

In a nutshell, we believe that the body will not reveal the full elegance of its design if we continue to see its movement from a lever/pulley muscular model. Just as Dr. Rolf needed to view the body from the vantage point of connective tissue in order to share her perceptions, we are offering a vision of walking that need not be either linear or segmented. Within this model, which we call “Natural Walking,”(1) movement is non-hierarchical with each aspect of the body and the design of joints and tissue participating in equal measure. As much as we agree with and appreciate the clarity and specificity that Gracovetsky has brought to spinal function in walking, we are seeking a view that integrates the elegance of spinal mechanics with the pelvis and legs.

Natural Walking is more than just our theory about walking. It is an understanding of human movement that can lead a principle-driven Rolfer’s diagnosis of structure and function, and assist in directing the Rolfer’s intervention. We are presenting much of this material in our classes. The technical details are important, but mostly we wish to emphasize that there is something here that is useful, practical, and true.

Three points are being raised for the benefit of creating further distinctions in a model of walking as we envision it and to stimulate further inquiry within our community. We then present theoretical and practical aspects of our Natural Walking model.

Questions About Gracovetsky’s Model

First, while Gracovetsky proved that the spine is essential to walking, we are not in agreement with his proof that walking can be accomplished without legs. His book The Spinal Engine(2) presents arguments and data that challenge that belief. It proposes that the spine is the primary engine that makes us move. His proof involves a video of a man who moves across the floor on his ischial tuberosities, as he was born without legs. This video is edifying in that it shows the great importance of the spine in ambulation and also shows an exaggeration of the spinal movements that accompany walking. However, it does not serve to switch the hierarchy of importance from the legs, as in previous physiological models, to the spine. The ischial tuberosities of the pelvis have never been classified as part of the spine. The fact that this man could walk was dependent on the first anatomical bifurcation that becomes the structure of two legs, the tuberosities. It is this structure that allowed that man to alternate weight bearing from one side to the next, just as we do from one leg to the next. So, while he was able to walk without the musculature of legs, he was dependent on the support of the vestige of a leg structure. Some paraplegics in leg braces also demonstrate a form of perambulation that depends almost solely on the movement of the spine, but this is in no way demonstrating a normal gait pattern. So, while we appreciate the new emphasis on the importance of the spine, we are no closer to a comprehensive understanding of this complex coordination that produces a normal biped gait.

Second, Gracovetsky went on, in his presentation, to describe the evolutionary development of the coordination between the spine and the girdles of a quadruped. His example was a lizard-like creature and its need to lift a leg up over a pebble. This action stimulates the rotational aspect of the spine that ultimately leads to our contralateral gait pattern. This is an elegant description for the development of this coordination pattern, but it does not address the particular problem for an upright mammal with only two legs to stand on.

In order to take the first step, a human or any animal in that position must figure out how to shift from a two-legged support to a single-legged support. This has to be the first initiation of movement into walking. For this to happen, there must be not a muscular lifting of the limb but a lateral movement that frees a limb from weight-bearing. Typically, this lateral movement is not initiated by the spine. The lateral movement of the spine is a response to a combination of a slight push off of one leg and a lateral movement of the opposite hip. This movement then frees the unweighted leg to lift up over that pebble or to take the first step. But an examination of the anatomical structure of the hip indicates that when the full weight is given into one hip and leg, the movement into that hip has to be not only lateral but rotational as well, unless muscularly inhibited. It is the offset of the head of the femur, which is not set in a directly lateral position, that engineers this combination of lateral and rotational response. We are contending that it is the anatomical structure of the hip and the proximity of the sacrum to this that draws the spine into a participatory side bend and rotational action – not that “. . . heel strike causes the side-bend of the spine which then rotates the pelvis.”(3)

While Gracovetsky’s model of the evolution of the coordination between the girdles and the spine makes complete sense, it does not address the particular challenge of a vertical stance to gravity and a support structure of two legs, not four. Again, the initiation of walking does not come from the lifting of a limb but from the shifting of weight that frees a limb to lift. And once the belly is off the ground, four-legged animals, such as horses, can be observed to do the same.

Third, we believe, after many years of observation, that unimpaired walking enlists full-body participation of the spine, shoulder and pelvic girdles, legs, arms and feet. Any inhibition against this participation results in muscular and/or skeletal strain, and over time, dysfunction. We further believe that we were designed to walk. By studying normal joint function, the clues to this full-body model of walking are clearly indicated. It is not only the spine that demonstrates the rotation, counter-rotation in concert with lateral movement as shown in Gracovetsky’s video.

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The Spiral Design of Nature and Man

Spirals are shown both in the shapes of the leg and arm bones and in the interaction between them at the joints. Even the fiber of muscles indicates spirals that interact in a double helix pattern to create springy tubes, set in a basket-weave pattern that offers a form of stored kinetic potential when released from weight-bearing. Rather than seeing distinct and isolated pulley action of muscles to move bones as levers, we see that walking is an orchestration of this kinetic-potential pattern in action. Simultaneously the body is in lateral, rotational, and a gathering, push/reach fluctuation along the vertical and sagittal plane. Gracovetsky’s model of the spring between two sticks that represented the spine between the two girdles demonstrated the lateral and rotational coordination but did not demonstrate the gathering and push/reach actions. These actions require the cooperation of the spine with the pelvis and legs, and are facilitated by the function of the psoas connection between them.

This coordination, which acknowledges the full-body spiral in action, is crucial if we are to see the potential for grace and balance during every phase of walking. This spiral, which is dictated by normal joint function, allows the torso to find balance first over one leg and then over the other. Without this principle, walking is precarious, as Gracovetsky said, and has moments that require extra exertion in order to rebalance or avoid falling.

In order to create a comprehensive, coherent, and efficient model for walking that also allows for variations in orientation and intent as well as personal proportions and styles, we need to look beyond the human being at a bigger picture. Just as Gracovetsky considered the evolution of locomotion and looked to the animal kingdom, we believe that nature provides insight both into the design of the body and the movements that indicate a model for walking. Consider that all of life depends on water and that our very tissue and bone were formed in the oceanic medium of the uterus. The current study of embryology clearly states that our form develops in response to the movement that comes first. What movement? Form follows the function of fluids as they meet the barrier of the container of the uterine wall and the force of gravity. This dynamic creates a spiral, a universal principal that can be observed within a glass of water as easily as in a flowing river. The tendency of free water to move in spirals is reflected over and over, from hurricanes to waterfalls to pictures of the galaxy.(4) And the shaping of matter as it is in interaction with fluid is seen from the shapes of seashells, throughout the plant kingdom, and into the details of human anatomy from the cochlea of the inner ear to the fibers of the heart muscle to the structure of DNA.(5) It seems almost hubris to ignore this universal pattern and to think that we are cut from a different cloth. The lever/pulley model of machines seems to have a hold still on Gracovetsky’s muscular model (the stick/spring imagery).

We feel that it is safe to assume that the spiraled shape of bones and tissue lends itself to a model of walking that follows this design. Especially since physics has indicated the efficiency of this design for storing kinetic potential as well as changing planes of action and responding to outside forces.(6) But the question remains: how do we see these spirals come together in natural, unencumbered walking? For the answer to that question we go to our collective experiences of observation coupled with a close look at the design inherent in our joint function.

Through our studies at the Rolf Institute of Structural Integration, we have come to appreciate the perfection of the design of the human structure for bipedal walking. Just as we are perfectly programmed and designed to breathe, so we are perfectly programmed instinctually and structurally to walk.

At almost every developmental movement stage – from rocking, to creeping, to crawling – a baby practices an essential element of walking. As we examine function of the arches of the foot, the knees, hips, spine, and pelvic and shoulder girdles, we find that each segment is designed to do its part in the whole body experience called walking.

This may not seem like a striking statement, but within the field of kinesiology (and more importantly within our culture), this has been neither the perception nor description. Walking has been viewed as controlled falling, and Gracovetsky has restated that view. The metaphor of action has been a machine of levers and pulleys that cause acceleration and then braking. Or, as in Gracovetsky’s presentation, a spring between two cross bars. We will be describing a system that at its most efficient is never out of balance, never has to inhibit the former action, stores angular momentum as efficiently as a Swiss watch spring, and mirrors a design found throughout the animal kingdom and nature.

We took efficiency as an operating principle of nature, a convention of physics that underlies all expression of natural law, most succinctly stated in Fermat’s Principle of Least Time and Maupertien’s Principle of Least Action(7) and thoroughly discussed in Feynman’s Lectures on Physics Vol. 2.(8) We found that we needed to step out of the traditional box of understanding walking. Our discovery was that human anatomy appears to demand a different pattern of gait than is commonly seen or theoretically understood in our Western culture. We are finding that the linear logic (cause and effect) of the industrial age produces a progressive error as we apply a two-dimensional model to our three-dimensional world. To quote Tom Myers: “Information is always lost when mapping from 3-D to 2-D.”(9) Therefore, a 2-D explanation of a 3-D event will always be in error.

It is time to move our model of walking out of the industrial age! Just as science has moved away from the billiard-ball picture of cause and effect towards a more fluid, interactive universe, we need a more fluid picture of ourselves, one that is a part of nature as a whole, not pitted against it. In order to do this it is helpful to view our anatomy differently, much as Tom Myers has presented in his Anatomy Trains.(10)

The Basket-Weave / Helix Theory

Let’s blur the distinction of individual muscles in isolated action, and see another design in the fibers. The individual fibers that make up all musculature lay along diagonals. Most of the discreet muscles also lay along diagonals. What begins to appear, if one gives up the idea of isolated muscle groups and allows muscles to transit boney structures is a pattern of diagonal lines.(11) Crossing spirals of muscular fiber become apparent. For example, a left pectoral muscle blends with a right intercostal that joins an oblique muscle that blends into a gluteal muscle.(12) This is exactly countered by a matching helix (a spiral in three-dimensions) from the right pectoral on down. Start at another point and the same type of helix emerges. An iliacus leads to a quadratus lumborum that wraps into the lattissimus on the other side of the body and so forth.

While tracking these patterns may defy our more linear, neat packaging desires, the overall picture of a double-helix pattern emerges; and in motion, counter-rotating helices. In other words, we are made up of muscular tubes of diagonal fibers that span superficial to deep and back out again. These transitions in depth are generally mediated through bones. Bones then assume a structural dimension that is in addition to levers and to spacers inherently more in tune with a tensegrity view of the body’s mechanics.

With the use of a couple of analogies, this new model can be appreciated. A machine that is designed for a consistent relationship to gravity is liable to sustain serious damage when forces outside its design-frame are applied to it. If this were indeed our design, few of us would survive our childhood in working order. Try putting a computer through the innumerable crashes of a typical youth and imagine what working order it might be in, to say nothing of its appearance.

To what do we owe our remarkable resilience? From football, to skiing, to tumbling we are able to sustain a tremendous array of reckless experiments and live to tell about it. Although our muscular tube design is not precisely an interweaving of diagonal fibers, as in a basket, the basket-weave analogy is helpful. For a certain generation this might bring to mind the straw “Chinese handcuffs.” These were tubes of woven straw that expanded when compressed and contracted when elongated, allowing one’s fingers to enter the tube from both ends but preventing the withdrawal of the fingers when they were pulled away. After either compression or elongation or twisting, the spiral double helix weave pattern will always return to its original shape by its own momentum. This model is closer to a spring than a lever/pulley model and reflects our spring-like resiliency.

Mathematics and the laws of physics define the efficiency of the helical model:(13,14)

1. A helix is the simplest form that requires three-dimensional space in order to be expressed.

2. A helix is the most efficient form to transition from one plane of action to another.

3. A helix has the most efficient kinetic storage potential. It can integrate both angular and linear momentum separately or simultaneously. A coil spring is the most obvious example of this property.

4. A helix is the most efficient form for storing sequential information. It is the form from which sequential data is most easily retrieved, i.e., DNA. The instantaneous correction and regulation of relationship depends on this efficiency.

In our view it is the model for homeostasis. The implications of a helical model are profound.

Returning now to the physical design of the body, many things make much more sense. It becomes easier to picture walking as a spiraling, counter-spiraling action of the whole body rather than seeing it as powered by a sequential series of lever/pulley actions. Although isolated muscular action is still very possible, the coordination of a whole body action becomes much more  self-evident. Walking becomes a milder form of the vast number of other actions we employ.

Running, throwing, kicking, swinging objects such as baseball bats or golf clubs, skiing – all are exaggerations of the overall coiling, spiraling, uncoiling, counter-spiraling action of walking. In other words, walking is the warm-up practice and the mild maintenance of the body’s capacity for these larger actions. How perfect!

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Taking the First Step

Given this new way of perceiving the body, what happens with the initiation of a step? From a two-legged stance, the first movement is not to flex a leg at the hip, but to shift weight bearing from two legs to one. This weight loads and compresses the joints of the support leg while the stride leg is released. As the pelvis shifts laterally to center over the support leg, the structural geometry of the offset head of the femur (the neck of the trochanter) causes the femur to medially rotate as it is weighted. This rotation is passively resisted by the stretching of the six lateral rotators of the femur on that side. This stretching protects the hip joint from over-rotating and damaging the joint, and initiates the side bending and rotating of the lumbar spine. This is another difference that we have with Gracovetsky regarding the primary action of the pelvis and legs. Meanwhile, at the knee, the close-packed position of the support leg allows the tibia to counter the medial rotation of the femur with a lateral rotation or, more precisely, a torque. So in only the preparation to take a step, ‘a spiral pattern is already in evidence in the boney structure and tissue response of pelvis and leg.’

Its continuation is assured in the upper body by the biomechanical design of the spine. This is where our model of walking is in agreement with Gracovetsky’s work. “As the masses decelerate, their kinetic energy becomes available for storage and later use during the next re-acceleration cycle of the masses. Elastic storage is possible not only in the muscles themselves but also in the spinal ligaments…”(15) And, we would add, the entire fascial web. The upshot of the above anatomical description is this: the spine will naturally respond to the compression of the support side and the release of the stride side according to these spinal mechanics. It will side bend and rotate. For example, if one were to stand into the left leg, the lumbar vertebrae will side bend left and rotate right. This facilitates the pelvis in the rotation that responds to the right leg swinging forward. Meanwhile, the thoracic spine will counter-rotate to the left. This happens to assist the torso in centering its mass over the support leg and the pelvic and shoulder girdle in coordinating a balanced counter-spiral. In other words the spiral action of the leg and pelvis is met and continued by the spine. It is possible to muscularly resist these responses but it takes extra effort to do so and the result is a more precarious balance. We also see that the movement of the upper body is part of ongoing balance, rather than playing catch-up in response to the loss of it.

All this just to prepare to take a step! And yet, the principles and mechanics of action remain the same. With the body well balanced over the support leg, the stride leg is free to swing forward. Its freedom from weight-bearing already initiates action, like a spring being released. The elastic recoil of muscular tubes already has momentum towards the new support leg, if not resisted. The coordination of hip flexors and the psoas muscle takes the femur forward. This begins a new side bend and counter-rotation of the spine, and the torso is in concert with shifting towards the new support leg. As one leg makes the transition from supporting to swinging, the release from weight-bearing compression, the elastic recoil of soft-tissue, and the mechanics of the hip joint all assist in the lateral shift that takes the body’s gravitational center from one hip to the other.

Because the knee, not the foot, has led the way into the next step, heel contact with the ground occurs before the leg is fully weight bearing. Should the footing turn out to be unstable, many self-correcting movements may be taken. By the time the body is balanced over this leg, the weight of the body is centered over the apex of the arch, which behaves like a shock-absorbing spring. The mobility of the twenty-six bones of the foot, plus the tibia and fibula of the lower leg, mediate the uneven surfaces of the earth to further enhance balance and protection against injury. This is quite different picture from “…heel strike cause the side-bend of the spine which then rotates the pelvis.”(16)

<img src=’https://novo.pedroprado.com.br/imgs/2009/1066-3.jpg’>

This picture demonstrates the spirals within the action of walking though it fails to show the hallmark of order, “the Line”, which would be present with better organization

The Elements Necessary for Good Coordination, Natural Walking

Many things can inhibit this design from operating smoothly. Footwear such as high heels, clogs, and flip-flops alter joint function and create certain holding patterns, while shoulder bags and backpacks inhibit the torso’s participation. Tight skirts dictate a short stride. Tight pants can inhibit pelvic response. From place to place and time to time cultural mores of what is cool, feminine, masculine, or modest will determine a style that is often learned completely unconsciously.

In order to see Natural Walking manifest there are certain elements that must be present. These are as follows:

1. The torso must be balanced over and supported by the leg(s). If the torso aligns itself either behind or ahead of the center of the pelvis, length, balance, and responsiveness are necessarily inhibited, whether standing or walking. Culturally, in the developed world, there is a predominant pattern of leading with the foot while holding back in the torso.

2. We are bipedal, which means we alternate our base of support from one foot to the other. If we allow our center of gravity to adjust helically from one support leg to the other, we gain support, balance, and fluidity of movement. Military marching and some other models of walking ask the center of the torso to be carried straight forward, like a flagpole, thereby inhibiting the response of the spine and overall torso. To hold against helical response actually requires more effort and impairs support, balance, and fluidity.

3. The counter-rotational coordination of pelvic and shoulder girdle must be evident. This contralateral action that is first practiced in our developmental phase of crawling, brings the arm swing into the overall coordination. However, unlike military marching, this arm swing is initiated by the spinal rotation response of the thorax as it finds center with the support leg. The arm swing is a follow-through of that action (as Gracovetsky also indicated in his presentation.)

4. Optimally, there is differentiation of function between the spine and the pelvic and shoulder girdles. This means that the spine is free to have its own coordinated participation in walking, distinct from the cross-crawl coordination of the girdles. During relaxed, slower ambulation a subtle forward/back undulate travels through the spine. This is the coiling/uncoiling mechanism carried through, and it mirrors the more easily remarked grace of the animal kingdom. If one watches the slow-motion replays of a satisfied athlete as he/she walks away from scoring, this undulate will show itself to be not dissimilar to that which a giraffe, leopard, horse, or many other four-legged creatures demonstrate in action. This was the “psoas walk” that Ida Rolf made paramount to a successful Rolfing series. However, this action is the first to be sacrificed to efficiency if we want to travel faster than a leisurely (most economic) pace.

5. The pelvis must find dynamic balance on top of the legs. Functionally, a horizontal pelvis must be able to rock with equal ease both forward and backward, like a chair suspended at the top of a Ferris wheel. If locked either anterior, shortening the low back, or posterior, holding the torso behind the legs, the psoas can not fully function and once again length, balance, and mobility will be impaired.

6. Responsiveness! When the whole body participates evenly and responsively, the attributes are grace, continuity of motion, subtlety, and unimpeded momentum. Holding against whole body participation in walking is always possible. This can occur anywhere – the neck, the diaphragm, the ankles, etc. Fluidity of motion is always lost, not just locally, causing the whole body to look segmented with still points in the action. It is a strange concept, but true, that still points require effort to be maintained in the middle of action.

7. Finally, in order for there to be optimum length in motion, which allows appropriate responsiveness, the impulse to move must be two-directional. To get off the ground, one must be able to simultaneously let down and lift off. Even a bird cannot fly unless it is able to push down on the wind with its wings while stretching upwards through its structure. When a person has a tendency to either rest down or hold up too much, length or responsiveness or both will be lost. Most people have a preference to initiate action either by reaching into space or pushing against the ground. In motion, integrated walking demonstrates the bi-directional impulse to simultaneously ground and lift. This means simultaneously pushing into the ground and reaching towards the sky.(17)

Developmental Preparation for Walking

During the stages of infant development, the separate components of this concert-in-motion are rehearsed individually revealing further the functional logic of this model of walking. It is as if these separate components get taken apart and practiced individually. Interestingly, these main stages of development mirror the evolution of the animal kingdom, from reptilian through amphibian and mammalian. Bonnie Bainbridge Cohen, a respected authority on the developmental movement of infants, has devoted a career to the study of these instinctually programmed patterns. Each one plays a role in organizing the nervous system and orienting a child spatially to the field of gravity and the surrounding environment. And each pattern, once mastered, leads the child to the next, more complex movement exploration, culminating in the ability to stand and walk on one’s own.(18)

Verticals and Horizontals Within This Model

As Rolfers we have observed that the more balanced and efficient a human body becomes, the closer the movement pattern demonstrates clear horizontal hinge action and vertical integrity through the segments. The center of hip, thigh, knee, calf and foot are in alignment and track straight ahead rather than at divergent angles. This has always been the cornerstone of Ida Rolf’s vision and theory. Therefore, the concept of helical actions seemed paradoxical. Rolf’s language of horizontal and verticals, however, does not deny helical structure and action. The basket weave analogy answers this seeming paradox. When one sees clearly cross-woven, balanced diagonal fibers forming an “X,” the verticals and horizontals become apparent. The degree of overall balance, seen in terms of the horizontal and vertical, is dictated by the relative balance of intersecting helices.

Review

The helical orchestration of human gait is composed of the following elements. First there is the compression and decompression of joints during the alternation of weight bearing and extension in movement. Second, there is the wringing, torquing, coiling and uncoiling of the muscular tubes. And third, humans mimic, but transcribe to the vertical, an aspect that all quadrupeds share, in the way that the limbs alternately gather towards center and then extend into forward motion. Picture a racing horse or a leaping cat. There is a gathering toward center that shortens the anterior (front of) spine as the limbs flex, followed by extension. In oriental martial arts this is sometimes called the coordinated closing and opening of joints. This mechanism, for lack of a better word, in a forward/back direction, combined with a whip like rotation, is the secret to great force and power that is derived from chi – energy and stored angular momentum – rather than muscular strength. When all of the above come together during walking what appears is a subtle undulate, the combination of yield, push, and reach, which combines forward/back, side bending, and contralateral movement. This wave motion travels through the spine in the sagittal plane without interfering with rotational or lateral responses. This coordinated spinal response that is also differentiated from the girdles is the hallmark of successful Rolfing Structural Integration. But at a faster pace, the spine and girdles will knit into a tighter unit of coordination for economy during speed.

If we refer again to the laws of spinal mechanics, we see that the spine is designed to cooperate, even assist, the diagonal coordination of side bending and rotating. The lumbar vertebrae of the low back will naturally work with the pelvis and legs, while the thoracic spine assists the action of the shoulder girdle. This causes a minimum of movement at the upper pole of the body and the cervical vertebrae of the neck are free to do whatever the sensing mechanisms of the head dictate – turning to look, listen, smell or speak – while allowing the vestibular system of the inner ear to do its job with balance.

The Benefits of the Natural Walking Model

Natural Walking, as efficient as a ticking watch, is practically a perpetual motion design, which uses the musculature of the body evenly and completely in cooperation with the gravitational field. Although it is only conjecture on our part, it makes sense, since there is no overt pumping mechanism for the lymph, venous, and micro-tubular systems, that this ordinary action should play a vital part in circulation. The compression-decompression wringing motion that we have described is perfect for allowing tissues and organs to be passively squeezed and refilled with new liquid.

Other benefits are as follows: the spine stays supple and resilient, its whip-like action able to defer shock and compression. With a functioning psoas and oblique muscles, toning and spanning of the mid-section are maintained more easily than is currently imagined in the fitness world of “core strengthening.” This is vital for the health of our visceral organs and lower back. With good alignment and use, joints remain strong and lubricated rather than breaking down under the wear and tear of uneven use. Walking becomes a perfect blend of exercise and relaxation, adjustable to various paces and intensities. Done well, it promotes balance to the system as one goes. Furthermore, since practically all other forms of exercise are simply exaggerations of the same physical mechanics, warm up and coordination is included, ready to be applied to other activities. All of this contributes to a more graceful, vital aging process. When this model is consciously experienced, one is less prone to chronic over-use type injury and often more able to vary movement patterns if fatigue or discomfort is starting to be felt. Simultaneous attunement to self and environment, increased stamina, and enhanced enjoyment of activity are all predictable outcomes. As Rolf said, “This is the gospel of Rolfing: When the body gets working appropriately, the force of gravity can flow through. Then spontaneously, the body heals itself.”

Endnotes

1. Ohlgren, Gael and David Clark, “Natural Walking.” Rolf Lines Vol. XXIII (Mar. 1995), pp. 21-29.

2. Gracovetsky, Serge, The Spinal Engine. New York: Springer Verlag, 1988, back jacket.

3. Ibid., pg. 307.

4. Schwenk, Theodore, Sensitive Chaos. East Sussex: Rudolf Steiner Press, 1996, pp. 13-141.

5. Gintis, Bonnie, Engaging the Movement of Life. Berkeley, CA: North Atlantic, 2007.

6. Saxena, A.K., Principles of Modern Physics. New York: Alpha Science Int’l., 1996, pg. 36.

7. Clark, Adam, Lectures on Physics, Allentown, PA: Muhlenburg College, 2009.

8. Feynman, R.P., R. Leighton and M. Sands, Feynman Lectures on Physics, Vol. 2. Reading, MA: Addison-Wesley, 1963.

9. Myers, Thomas, Anatomy Trains, 2nd ed. New York: Churchill-Livingstone, 2008.

10. Ibid.

11. Schwenk, op. cit., pg. 25.

12. Ibid.

13. Willson, Frederick, Descriptive Geometry – Pure & Applied. New York: MacMillan, 1898, pp. 39-40, 122-123, 188-193.

14. Vinogradoved, I.M., ed., Encyclopedia of Mathematics. Dordrecht, Netherlands: Kluver Academic Publishers, 1989, pp. 398-400.

15. Gracovetsky, op cit., 1988.

16. Ibid., pg. 307.

17. Notes from a lecture on movement by Hubert Godard, Boulder, CO, 1999.

18. Notes from a class with Bonnie Bainbridge Cohen, Boulder, CO., 1987.

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. Myers, Thomas, Anatomy Trains, 2nd ed. New York: Churchill-Livingstone, 2008.

. Ohlgren, Gael and David Clark, “Natural Walking.” Rolf Lines Vol. XXIII, Mar. 1995.

. Saxena, A.K., Principles of Modern Physics. New York: Alpha Science Int’l., 1996.

. Schwenk, Theodore, Sensitive Chaos. East Sussex: Rudolf Steiner Press, 1996.

. Suzuki, Ryohei, ed., Human Adult Walking – Primate Morpho-physiology. Tokyo: University of Toyko Press, 1985.

. Vinogradov, I.M., ed., Encyclopedia of Mathematics. Dordrecht, Netherlands: Kluver Academic Publishers, 1989.

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Co., 1977.

. Wilson, Frederick, Descriptive Geometry – Pure and Applied. New York: MacMillan, 1898.A Rolfer’s Response to Gracovetsky[:]